Systemic metabolic reactions are obtained by singular value decomposition of genome-scale stoichiometric matrices

Genome-scale metabolic networks can be reconstructed. The systemic biochemical properties of these networks can now be studied. Here, genome-scale reconstructed metabolic networks were analysed using singular value decomposition (SVD). All the individual biochemical conversions contained in a reconstructed metabolic network are described by a stoichiometric matrix (S). SVD of S led to the definition of the underlying modes that characterize the overall biochemical conversions that take place in a network and rank-ordered their importance. The modes were shown to correspond to systemic biochemical reactions and they could be used to identify the groups and clusters of individual biochemical reactions that drive them. Comparative analysis of the Escherichia coli, Haemophilus influenzae, and Helicobacter pylori genome-scale metabolic networks showed that the four dominant modes in all three networks correspond to: (1) the conversion of ATP to ADP, (2) redox metabolism of NADP, (3) proton-motive force, and (4) inorganic phosphate metabolism. The sets of individual metabolic reactions deriving these systemic conversions, however, differed among the three organisms. Thus, we can now define systemic metabolic reactions, or eigen-reactions, for the study of systems biology of metabolism and have a basis for comparing the overall properties of genome-specific metabolic networks.